Pregunta
Q.7.2 Test (CST): Trigonometry Question 12 of 25 Which symbol correctly compares the two angles? \( \begin{array}{l}\frac{\pi}{3} — 30^{\circ} \\ \text { A. }< \\ \text { C. }= \\ 1\end{array} \)
Ask by Vargas Pena. in the United States
Jan 31,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The correct symbol to compare \( \frac{\pi}{3} \) radians and \( 30^\circ \) is \( > \).
Solución
To compare the two angles \( \frac{\pi}{3} \) radians and \( 30^\circ \), it's easiest to convert both angles to the same unit. Let's convert \( \frac{\pi}{3} \) radians to degrees:
\[
\frac{\pi}{3} \text{ radians} = \frac{\pi}{3} \times \frac{180^\circ}{\pi} = 60^\circ
\]
Now, compare the two angles:
\[
60^\circ \quad \text{and} \quad 30^\circ
\]
Clearly,
\[
60^\circ > 30^\circ
\]
Therefore, the correct comparison symbol is \( > \).
**Answer:** \( > \)
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Simplifique esta solución Bonus Knowledge
Did you know that \(\frac{\pi}{3}\) radians is equivalent to \(60^{\circ}\)? This means that when you compare \(\frac{\pi}{3}\) to \(30^{\circ}\), you can see visually that \(60^{\circ}\) is definitely greater than \(30^{\circ}\)! So the correct symbol here is \(>\). When converting radians to degrees, a common mistake is forgetting the relationship that \(180^{\circ}\) equals \(\pi\) radians. To convert radians to degrees, use the formula \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\). This is super handy for comparing angles!
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